Nineteen of Medvedev's twenty-one titles have been achieved on hardcourt
A comeback the Russian player won his first championship for over two years with success over opponent Moutet in the Almaty Open championship match.
Medvedev, a ex- world number one, has had a torrid season, winning just one win at the big events and undergoing a difficult moment at the American major.
His varied form on the professional circuit - and issues with his serving in especial - led to him dropping out of the top ten and eventually splitting with long-term coach Gilles Cervara.
Presently training with Thomas Johansson and his other coach, he has consistently improved in the past month - climaxing in a hard-fought 7-5 4-6 6-3 victory over opponent Moutet.
This marks his first trophy after the Rome competition and initial on a hard surface from spring of 2023.
Success also means Medvedev has won 21 victories at twenty-one distinct events.
"It's the first time I'm at a tournament with my both daughters together, so to win a title is really nice," stated world number 14 the champion.
"This title is in dedication of my second daughter her name, because the maiden victory I won when my first daughter her name was born was for her."
The athlete, the 2021 US Open champion, had lost his previous six championship matches, including in the German tournament in the past months.
Medvedev's defensive play style and frequent outbursts on court had led commentators to wonder if his capacity to play at the highest level was finished.
However the 29-year-old has made changes in the past month, attempting to come to the net and play aggressively, supported by an better serving game.
Medvedev recovered from a disadvantage in the opening set against the tricky Frenchman, securing four of the last five games to go ahead.
Both players swapped breaks in the second set before Moutet, striving for his first tour title, seized the initiative to create a decider.
The opponent saved four early-game break points in a close third set before Medvedev won the break to fifteen to secure the win.
Suitably, Medvedev earned the title with a point at the net area, with the Frenchman unable to handle a volley after a lengthy match.
